are to design a GUI control interface for optimal control, which has good human-computer interaction interface and is easy to use. Linear quadratic optimal control, also known as LQ optimal control or state regulator for infinite time steady state systems, is implemented in MATLAB. This paper presents four research schemes on the implementation of continuous system linear quadratic optimal control in MATLAB, discrete system linear quadratic optimal control in MATLAB, optimal observer in MATLAB, and linear quadratic Guass optimal control in MATLAB. The paper designs different GUI interfaces and programs for each of the four aspects to achieve different performance indicators and explains their respective application ranges. Keywords: linear quadratic, optimal control, GUI control interface, optimal observer, Guass optimal control. This paper aims to provide a comprehensive overview of the implementation of linear quadratic optimal control in MATLAB, with a focus on the design and development of GUI control interfaces for optimal control systems. The paper covers topics such as the use of MATLAB software for designing GUI control interfaces, the implementation of linear quadratic optimal control in both continuous and discrete systems, and the design of optimal observers and linear quadratic Guass optimal control in MATLAB. The paper also discusses the various performance indicators used in the design of the GUI interfaces and explains the application ranges of each of the four research schemes. In conclusion, this paper serves as a valuable resource for researchers and engineers looking to implement linear quadratic optimal control in MATLAB, providing insights into the design and development of GUI control interfaces and their respective applications in optimal control systems.